Here’s a thought. A barking dog would look better than a nodding dog. With that in mind I have made some modifications to the nodding dog model that I made with the Eclips2 paper cutter

Here’s the prototype. I’ve cut away the body and recessed the lower jaw into the slot. The lower jaw will remain stationary while the upper jaw moves up and down.

Here’s the movement in action. Looks promising I think.
I’m planning on releasing the final as both a normal download-cut-out-and-make kit as well as an svg file for those of you with cnc paper cutters.